Re: "A third country might offer a new couch"
Of course if that pilot is a foreign national on a diplomatic passport brought in specially for the job, then there's not a whole lot they could make stick
Diplomatic immunity doesn't work like that. You don't just get a diplomatic passport and a free chance to go anywhere and do anything you want.
Diplomatic immunity has to be granted in advance.
Although there are circumstances where it applies to people in transit (such as to UN meetings) so the US can't stop people it doesn't like going to the UN - even though it's in New York.
That's why Ecuador can't just give Assange one of their own diplomatic passports and that be a get out of jail free card.
A country could get a normal diplomatic posting for someone who just happened to be a chopper pilot though, but the FCO might expel a bunch of their diplomats in a fit of pique for a stunt like that.